The distance between the function image and two adjacent intersections of a straight line y=2 is equal to π.
∴ Function period T=π=2π/w
∴w=2
∴f(x)=2sin(2x+π/6)
Let -π/2+2kπ≤2x+π/6≤π/2+2kπ.
k∈Z
We get: kπ-π/3≤2x+π/6≤kπ+π/6.
k∈Z
The answer should be C.